Revisiting this. Isn't it a bit of a red herring to enquire about the number of 2-faces that an n-simplex has? It still only has n+1 vertices. A 768-simplex may have 75.5 million faces but it will still only have 769 vertices which completely define the shape. So why would I expect a large number of the other >90% of the 10,000 samples I have to lie on the surface, rather than inside the interior volume?
To be more direct, what's the specific relevance of bringing up the number of 2-faces that an n-simplex has?
To be more direct, what's the specific relevance of bringing up the number of 2-faces that an n-simplex has?